In other words, you have to model or get the mathematical equivalent of the real-world transfer function of the amplifier. With this equation, you look at the denominator (usually a polynomial), do factorization and figure out the values that will zero-out the equation. These are your poles, and their values tell you if the amp is stable or not... I left this behind when I realized you can't figure out the math equation without measuring the amp - and if you do 'measure up' the amp, you may as well find out if its stable or not from there...

Pole/zero pairs are quite useful in the theoretical domain for modeling amplifier stability and phase/amplitude responses. I find them extremely tedious to interprete and hardly ever use them and I am a full time analog design engineer. They will tell you quickly whether or not the circuit is stable based on what plains the poles, and zeroes inhabit, beyond that it is somewhat difficult to interprete.

I recommend instead that you download spice and learn how to use that instead, you will much more quickly arrive at results that you can use. LTspice/SWcadIII is an excellent choice as you can add competing device models and tubes as well quite easily.

Let's look at a simple lowpass filter. A resistor in series followed by a capacitor to ground. The transfer function is:

Vo/Vi = Xc / [Xc + R]

Vo/Vi = [1/(2*pi*f*C)] / [(1/(2*pi*f*C)) + R]

Vo/Vi = 1 / [ 1 + (2*pi*f*C*R) ]

At DC, f = 0, the transfer function equals 1. As f increases, the value of the transfer function decreases... where 2*pi*f*R*C equals one in the botton of the equation; this is location of the pole... the -3dB point.

Below is the frequency response of the "electronics" of the popular radioshack sound level meter(digital). My goal is to extend the high and low frequency rolloffs further out, without adversely affecting the gain (and hence the calibration of absolute spl) of the meter.

If you would like to take a look at the schematic of the meter which another enthusiast has drawn up then its here -

Now how do I identify which networks, and components within those networks, are causing the rolloffs ? I can look at the schematic and identify some networks right away especially in the input section that the coupling caps are undervalued but how can I make sure I covered them all ? and thats where pole analysis came in.

It could also be the IC (LM324) that is rolling off but someone in the chipamp forum said that its not likely and I dont want to go about replacing ICs without really making sure it will help. So baiscally I just want to sort out the areas which are causing this rolloffs. Hope that helps.

Generally math(algebra, trig) doesn't intimidate me. Now calculus is something I wasn't really friends with but that was at a time when I didn't have access to calculators that could do calculus!
I am still encouraged to try it though.

c2, c5, c6, c7, c11, c12 are poles these could all stand to increased by a factor of 3 or more... in nearly all cases the method for arriving the value of R is different. Google Thevinen equivalents and find the AC resistance of the node the caps is hooked to.

c4, c9, c12 are zero's and you must do the same thevinenthing but there are op-amps involved so "AC grounds" are less clear.

C13 and its network does something whacky but I don't know what.

C18 is the filter for the peak detector and should left as is.

I would start by just working on the poles and then measure it again.

Kevinkr's idea about getting LTspice is a good one two.

Most of the BS hanging "below" the op-amps is for bias and can be ignored.

I agree with kevinkr, just plug the circuit into LTSPICE and start modifying the capacitors. Put two versions of the circuit on one schematic page, so that you'll always have a reference output to compare against.

The C13 network seems to be an output coupling network (to a jack?) so I think that can be ignored...